Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then :
g'=3g
g'=\(\frac{g}{9}\)
g'=9g
g'=\(\frac{g}{3}\)
The Correct Option is A
Solution and Explanation
Let the mass and radius of the new planet be M′ and R′, then for same density as earth,
R′=3R
M′=27M
we know M\(\propto\)V, where V\(\propto\)R3
For Earth
g=\(\frac{GM}{R^2}\) (1)
and for new planet
g'=\(\frac{GM'}{R^2}\)
=\(\frac{G(27M)}{(3R)^2}\)
=\(3\bigg(\frac{GM}{R^2}\bigg)\)=3g
\(\Rightarrow\) g'=3g
Therefore, the correct option is (A): g'=3g
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].